We give a short introduction to the stochastic calculus for Itô-Lévy processes, and review brie‡y the two main methods of optimal control of stochastic systems described by such processes, namely: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated adjoint backward stochastic di¤erential equation (BSDE). The two methods...

This paper deals with development and analysis of a fully discrete nite element method for a nonlinear di erential system for describing an air water system in groundwater hydrol ogy The nonlinear system is written in a fractional ow formulation i e in terms of a saturation and a global pressure The saturation equation is approximated by a nite element method while the pressure equation is trea...

colleagues [1] exploring the value of cytochemical markers for the diff erential diagnosis of meningitis in patients with a Gram-negative direct cerebrospinal fl uid (CSF) examination. We have some concern as regards the confounding factors in their study. Firstly, although lumbar puncture was performed immediately on patient admission, the timepoint to obtain the CSF samples relative to the on...

Litt le is known about the acquisition of another language modality on second language (L2) working memory (WM) capacity. Diff erential indexing within the WM system based on language modality may explain diff erences in performance on WM tasks in sign and spoken language. We investigated the eff ect of language modality (sign versus spoken) on L2 WM capacity. Results indicated reduced L2 WM sp...

Fractional calculus is a natural extension of the integer order calculus and recently, a large number of applied problems have been formulated on fractional di¤erential equations. Analytical solution of many applications, where the fractional di¤erential equations appear, cannot be established. Therefore, cubic polynomial spline function is considered to …nd approximate solution for fractional ...

We consider the di?erential equation f<sup>''</sup> +A(z)f<sup>'</sup> +B(z)f = 0, where A(z) and B(z) are entire complex functions. improve various restrictions on coe?cients prove that all non-trivial solutions of in?nite order.

Examining the visual fi elds is an integral part of any ophthalmic evaluation. All ophthalmologists ordering and interpreting visual fi elds should go through the experience of having visual fi eld tests done on them, and also perform some tests on patients themselves. This may help them better understand and use the diff erent perimeters available, and improve their communication with their te...

The concept of pain has evolved from that of a one-dimensional sensation to that of a multi-dimensional experience encompassing sensory, discriminate, cognitive, motivational and aff ective qualities. Pain is the presenting symptom of a broad spectrum of diseases that needs to be diagnosed and treated. Establishing a precise diagnosis and providing eff ective treatment have become major challen...

In this study we analyze a non-overlapping domain decomposition method for the solution of elliptic Partial Di erential Equation (PDE) problems. This domain decomposition method involves the solution of Dirichlet and Neumann PDE problems on each subdomain, coupled with smoothing operations on the interfaces of the subdomains. The convergence analysis of the method at the di erential equation le...